# Spot Rates

Hey guys, I keep running into this problem where it asks for the current market price of a bond maturing in X amount of years. Then gives you like 5 treasury spot rates or so. My question is how do you know when you have to use just the spot rate that corresponds to the yr in the question or all of the spot rates to discount back the bond? Also when would you use the forward rates? only when they ask for that specifically?

Question says: Based on the info provided in the table (gives you 5 spot rates and 5 credit spreads), the current mkt price of a \$1000 par value, option-free, 0% coupon corporate bond maturing in 5 yrs is closest to: When you have to discount the bond using all of the rates, rather than just yr 5? Also, if it said that it was not a zero coupon pay bond, would you have to add the par value with the coupon payment, then divide by the spot rate? Thanks

If it had coupons you would need the spot rates to discount the coupons. Since it doesn’t have coupons, you don’t need the intermediate rates.

I know the question you’re referring to. You simply discount it using the 5yr spot rate PLUS the credit spread because it’s a corporate and not a Treasury.

thanks Joey, I just looked it up. If it asks for the arbitrage free value then u have to use all spot rates.

Huh? You don’t need (or can even use) the 3-yr spot rate if you are valuing a 5-yr zero.

Yea, only a coupon paying bond requires the intermediate rates. Remember, you are discounting the future cash flows, and a zero coupon bond only has two cash flows: at issuance and maturity.

I was getting confused on why sometimes u use all the spot rates to get the value of the bond and sometimes u only use one spot rate, like the example above and now below, "Based on the info provided in the table (gives you 5 spot rates and 5 credit spreads), the current mkt price of a \$1000 par value, option-free, 0% coupon corporate bond maturing in 5 yrs is closest to: " I was unsure on why you have to just use the 5 yr spot rate as opposed to using all the spot rates to discount the bond

Thanks Bp, that makes sense